Abstract

Interactive generative art module driven by real-time quantum mechanical computation: massively parallel eigenvalue decompositions of random Hermitian matrices displayed as rotating kaleidoscopic eigenvector projections. Minkowski spacetime diagrams with Lorentz-boosted reference frames, Schrödinger wavefunction evolution with uncertainty spreading, double-slit interference with which-path erasure, Bloch sphere qubit precession, Fock space ladder operators, Stern–Gerlach spin separation, EPR entanglement visualization, particle elastic collisions with phase-space trajectories, Dirac comb reciprocal lattice, energy level diagrams, and additive synthesis audio via Web Audio API eigenvalue harmonics. Press SPACE, click, or tap to fully randomize all parameters and color palettes.

Mathematical Foundation

The Schrödinger equation iℏ∂ψ/∂t = Ĥψ governs wavefunction evolution. Eigenvalue decomposition Ĥ|n⟩ = Eₙ|n⟩ yields energy eigenvalues extracted via QR iteration with Wilkinson shifts. The Minkowski metric ds² = c²dt² − dx² − dy² − dz² defines spacetime intervals. Lorentz transformations with rapidity φ = arctanh(v/c) boost between inertial frames. Von Neumann entropy S = −Tr(ρ log ρ) measures quantum information. Bloch sphere coordinates θ,φ parameterize qubit states |ψ⟩ = cos(θ/2)|0⟩ + e^{iφ}sin(θ/2)|1⟩. Fock space ladder operators a†|n⟩ = √(n+1)|n+1⟩ create particle number states. Heisenberg uncertainty ΔxΔp ≥ ℏ/2 bounds simultaneous observables. EPR Bell state |Ψ⁻⟩ = (|↑↓⟩−|↓↑⟩)/√2 models entanglement.